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A combinatorial approach to prove an explicit form of some iteration groups |
Aequationes mathematicae 99(6), 2797-2806 (2025). DOI 10.1007/s00010-025-01191-4.
Abstract. An example of some iteration group in a ring of formal power series over a field of characteristic 0 is given in Aeq. Math. 98(3), 837-850 (2024). It is proved under the hypothesis that some system of combinatorial identities is valid. Here we discuss a proof that the mentioned system of identities is indeed satisfied. It is based on the Chu-Vandermonde identity. From this result we obtain an explicit formula for some one-parameter group of (truncated) formal power series. Moreover we describe some non-commutative groups of solutions of the third Aczél-Jabotinsky differential equation in the ring of truncated formal power series.
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GDPR | A combinatorial approach to prove an explicit form of some iteration groups |  |